MinT - Information on Result #2612829

Information on Result #2612829

Linear OOA(2¹⁴², 50, F₂, 3, 96) (dual of [(50, 3), 8, 97]-NRT-code), using strength reduction based on linear OOA(2¹⁴², 50, F₂, 3, 98) (dual of [(50, 3), 8, 99]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁸, 10, F₁₆, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁸, 16, F₁₆, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)), using
    - Reedâ€“Solomon code RS(8,16) [i]
2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁴³, 50, F₂, 3, 96) (dual of [(50, 3), 7, 97]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁴², 25, F₂, 6, 96) (dual of [(25, 6), 8, 97]-NRT-code)	[i]		OOA Folding